p-Converging operators and Dunford-Pettis property of order p

In the present paper, a new concept of weakly p-Cauchy sequences is introduced to study p-converging operators and Dunford-Pettis property of order p. The notion of p-(V) sets is defined to characterize Dunford-Pettis property of order p. We also introduce a complete locally convex topology by relatively weakly p-compact sets to quantify Dunford-Pettis property of order p.